Let R be a commutative ring with unity and M be a non zero unitary left R-module. M is called a hollow module if every proper submodule N of M is small (N ≪ M), i.e. N + W ≠M for every proper submodule W in M. A δ-hollow module is a generalization of hollow module, where an R-module M is called δ-hollow module if every proper submodule N of M is δ-small (N δ  M), i.e. N + W ≠M for every proper submodule W in M with M W is singular. In this work we study this class of modules and give several fundamental properties related with this concept
Let M be a R-module, where R be a commutative ring with identity, In this paper, we defined a new kind of module namely ET-hollow lifting module, Let T be a submodule of M, M is called ET-hollow lifting module if for every sub-module H of M with
The current study involves an experimental investigation of plasma main parameters of a DC discharge with a hollow cathode (HCD) geometry in air using apertures of different diameters from the hollow cathode (1, 1.5, 2, and 2.5 cm). A tiny Langmuir probe is used to investigate the plasma properties. The HCD was operated at constant power of 12.4 W and gas pressures ranging between 0.1 to 0.8 torr. It was observed that the operational conditions strongly affect the electron temperature and density, while the hollow cathode diameter has not much influence. The main important observation was that at relatively high air pressure (>0.4 torr) two electron temperatures were obtained, while at relatively low pressure (<0.4 torr)
... Show MoreLet be a commutative ring with unity and let be a non-zero unitary module. In
this work we present a -small projective module concept as a generalization of small
projective. Also we generalize some properties of small epimorphism to δ-small
epimorphism. We also introduce the notation of δ-small hereditary modules and δ-small
projective covers.
Let
be an
module, and let
be a set, let
be a soft set over
. Then
is said to be a fuzzy soft module over
iff
,
is a fuzzy submodule of
. In this paper, we introduce the concept of fuzzy soft modules over fuzzy soft rings and some of its properties and we define the concepts of quotient module, product and coproduct operations in the category of
modules.
Let R be a commutative ring with identity. R is said to be P.P ring if every principle ideal of R is projective. Endo proved that R is P.P ring if and only if Rp is an integral domain for each prime ideal P of R and the total quotient ring Rs of R is regular. Also he proved that R is a semi-hereditary ring if and only if Rp is a valuation domain for each prime ideal P of R and the total quotient Rs of R is regular. , and we study some of properties of these modules. In this paper we study analogue of these results in C.F, C.P, F.G.F, F.G.P R-modules.
The corrosion behavior and corrosion inhibition of α-brass (65.3% Cu, 34.4% Zn and others 0.3%) in 0.6 mol.dm-3 NaCl solution have been investigated using potentiostatic polarization technique, the main results obtained were expressed in terms of corrosion (Ec) and corrosion current (ic). The research was performed in neutral and slightly acidic media [pH=7 and pH=4] over the temperature range (288-318)K. It was found that the rate of corrosion increases with the increase of acidity and the increase of temperature. The rate of corrosion increased with the increase of temperature in conformity with Arrhenius equation. Values of activation energy (Ea*), pre-exponential factor (A) and entropy of activation (∆S*) have been derived f
... Show MorePPSU hollow fiber nanofiltration membranes are prepared by applying two concentrations and various extrusion pressures according to the phase inversion method. Cross-sectional area and outer structures were characterized by using scanning electron microscope (SEM) and atomic force microscopy (AFM). In additional to the pore size distribution, either the mean roughness or the mean pore size of the PPSU hollow fiber surfaces was evaluated by AFM. It was found that the morphology of the PPSU fibers had both sponge-like and finger-like structures through different extrusion pressures and PPSU concentrations. The mean pore size and mean roughness for inner and outer surfaces were seen to be decreased with the increase of extrusion pressure at
... Show MoreLet be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.
5-(mercapto-1,3,4-thiadiazole-2yl)α,α-(diphenyl)methanol have been synthesized by ring closer of potassium xanthate[which have been prepared by reaction of benzilic acid hydrazide with carbon disulphide in potassium hydroxide] using conc.sulphuric acid at (0-5)°C scheme(I). Their characterization was carried out from T.L.C, M.P, FT.IR and 1H-NMR.
In this paper, we introduce a type of modules, namely S-K-nonsingular modules, which is a generalization of K-nonsingular modules. A comprehensive study of these classes of modules is given.